## Mathematics to enjoy art

25 de febrero de 2013 | Por | Categoría: Café de sastre

Por Carlos Usón Villalba.

When a person watches an Islamic decoration like this, it’s normal to feel bewilderment and perplexity because it’s abstract, but not only because of that. It’s simple and complex at the same time and the infinity is present inside.

Repetition is its principal argument and infinity is its aim. That aspiration of infinity is disconcerting, the repetition is absorbent and its obsession for filling entire plane overwhelms.

But, beyond the sensations and emotions, the bewilderment continues and the mind needs keys to understand. This is the raison of this article: To provide mathematical keys, necessaries to understand this designs.

If you’d love to paint an infinite picture, you could draw an infinite landscape but at some point you feel tired or you are lazy and you decide to repeat the design, you only have seventeen different ways of finishing it. Seventeen algebraic structures called symmetry groups. The raison of this is repetition in itself. There are only four movements in the plain: translation, reflection, rotation and sliding. But if you move a design and after that you reflect (or slide or turn) it as often as you want, the new design will be always the first one: rotated, moved, reflected or slid. The repetition allows few possibilities to run away.

Each one of Islamic design is one of these seventeen models. The Islamic artists didn’t know that but they didn’t mind. They didn’t need it to understand or to draw. We do. They were building an art at religion serve, where the repetition and the lines interweaved were looking for the unity of multiplicity, suggesting the infinite and evoking Ala. They were drawing with patterns but the trial and error method made it possible to find the seventeen possibilities.

Then, where is mathematical analysis utility? Each one of these seventeen symmetry groups has different geometric and aesthetic meanings. It’s important to know their meanings to understand the artist’s aim when he chooses one or another symmetry group because he chooses the aim and the aim “chooses” the group.

Carlos Usón Villalba (1st of intermediate level)

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